Chapman Inc.\'s Mexican subsidiary, V. Gomez Corporation, is expected to pay to

Question

Chapman Inc.'s Mexican subsidiary, V. Gomez Corporation, is expected to pay to Chapman 50 pesos in dividends in 1 year after all foreign and US taxes have been subtracted. The exchange rate in 1 year is expected to be 0.10 dollars per peso. After this, the peso is expected to depreciate against the dollar at a rate of 4% a year forever due to the different inflation rates in the US and Mexico. The peso-denominated dividend is expected to frow at a rate of 8% a year indefinitely. Chapman owns 10 million shares of V. Gomez.

What is the present value of the dividend stream, in dollars, assuming V.Gomez's cost of equity is 13%?

Kindly provide solution equation.

Thank you very much!

Explanation / Answer

dividend at r years = 50 pesos * (1+8%)^(r-1)

In dollars = 50 pesos * (1+8%)^(r-1) * 0.10 $/peso /(1+4%)^(r-1)

Present value of this dividend in dollars ={$ 50 * (1+8%)^(r-1) * 0.10 /(1+4%)^(r-1)} / (1+13%)^r

Present Value of Dividend Stream = 10 million * ($ 50 * 0.10) * [{(1.08/1.04)^0 / 1.13^1}^ + {(1.08/1.04)^1 / 1.13^2}+{(1.08/1.04)^2 / 1.13^3}+...] = [10 million * ($ 50 * 0.10) / 1.13}] * (1+{(1.08/1.04) / 1.13}^1+{(1.08/1.04) / 1.13}^2+...) = $ 546,218,487.4 = Answer

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